Discrimination thresholds for a pair of vertical lines are typically very precise, but increase dramatically when these lines are connected to form a closed figure (McKee, 1983, Vision Research, 23, 191-198). Here we explore the possibility that degradation in performance reflects depth averaging, brought about by mid-level grouping operations. To this end, we assess suprathreshold depth magnitude percepts for a set of stimuli which provide consistent local disparity information, while their interpretation as part of an object is manipulated. We presented four equally spaced vertical lines and observers judged the relative depth of the central pair in three conditions: (i) isolated lines, (ii) within an object (connecting central pair with horizontal lines), and (iii) between two objects (connecting central lines with outer lines). We used a precisely calibrated pressure-sensitive sensor to record the perceived depth separation of the central lines. In a second experiment, we evaluated the impact of conflicting perspective on the strength of the effect. Our results show a strong and consistent reduction in the relative depth estimated within an object relative to the isolated line condition. Further, this loss of depth magnitude is eliminated in the between object condition, and estimates return to the levels found for isolated lines. Manipulation of perspective cues did not affect this pattern of results. Taken together, our results show that figural grouping is a strong determinant of the amount of depth perceived in simple stimuli. These findings extend existing research that has shown threshold performance to be susceptible to configuration. However the extension of this influence to suprathreshold estimates of depth magnitude is notable, and suggests that within-object disparities are subject to a form of depth averaging that enhances their perceived cohesiveness. When these identical components form the edges of separate objects, this averaging does not occur, thus promoting object segregation.